Acoustical source and transducer having, and method for, optimally matched acoustical impedance

ABSTRACT

The invention, in its several embodiments, includes a method of making a plurality of impedance-matched layers interposes between an acoustical source and a target media providing optimal transmission of energy from the acoustical source to the target media.

BACKGROUND

[0001] 1. Field of the Invention

[0002] The present invention relates generally to acoustical sources andultrasonic transducers and particularly to ultrasonic transducers havingoptimally matched acoustical impedance and methods of achieving optimalacoustical impedance matching for such devices.

[0003] 2. State of the Art

[0004] When an acoustical source transmits a signal into a targetmaterial, much of the energy is lost when there is an acousticalmismatch between the source and the target. For example, in medicalultrasonics, a typical piezoelectric ultrasonic source, such as atransducer, has an acoustical impedance of about 34×10⁶ Kg/m²·s whilethe human body, in this case the target, has an acoustical impedancesimilar to water which is 1.5×10⁶ Kg/m²·s. As is known in the art, theenergy reflection coefficient is given by the difference in the twoimpedances divided by the sum of the two impedances and then theresulting quantity is squared. Such an acoustical mismatch results inapproximately 84% of the energy being reflected at the tissue-transducerinterface. For the above example, the energy reflection coefficient isabout 0.84, which means that about 84% of the incident energy will bereflected. This serious problem is overcome by placing what is known asa “quarter-wavelength matching layer” between the tissue and thetransducer. Such a layer, mounted to the face of the piezoelectriccrystal, has an acoustic impedance that is the geometrical mean of theimpedances of the source and the target tissue and has a thickness thatis equal to a multiple of a quarter-wavelength of the acoustical wave inthe matching layer. Symbolically, let Z₀ represent the acousticalimpedance of the piezoelectric crystal and Z₂ represent the acousticalimpedance of the target tissue. Then the impedance of the matchinglayer, Z₁, is given by

Z ₁=(Z ₀ Z ₂)^(1/2).  [1]

[0005] The thickness of the matching layer, L₁, is given by

L ₁=(2n−1)λ₁/4,  [2]

[0006] where λ₁ is the wavelength of sound in medium 1 and n is aninteger.

[0007] The theoretical basis for a quarter wavelength matching layer iswell known in the art and well described in the acoustical literature,the literature associated with ultrasonic engineering, and theliterature associated with medical imaging, representing a solution to aclassical boundary value problem in acoustics in which a plane wavetravels from one medium into another though an intermediate layer. Thesolution to this boundary value problem is such that if the intermediatelayer meets the conditions of Equations 1 and 2, then 100% of the energypropagating in the first medium will be transmitted into the second.Although this analytical result is strictly valid for only a singlefrequency, experimental results reported in the field have shown thateven broad-band devices with a wide spectrum of frequencies greatlybenefit from the use of such a matching layer.

[0008] The quarter wavelength matching layer provides a viable solutionif the mismatch in impedances is not too large. For example, in themedical ultrasonics case given above Equation [1] yields a matchinglayer impedance of about 7×10⁶ Kg/m²·s. This impedance is known topractitioners in the field to be well within the range of several rubberand plastic materials that could be used for a matching layer. Suchsingle layer matching layers are widely used today in medical andindustrial applications of ultrasound.

[0009] If, on the other hand, the mismatch in impedances between the twomaterials is large, the quarter-wavelength matching layer no longerprovides a practical solution. For example, if it is desired to match atypical piezoelectric transducer having an impedance of 34×10⁶ Kg/m²·sto air having an impedance of 415 Kg/m²·s, then, using the relationshiprepresented by Equation 1, a single matching layer would be requiredhaving an impedance of 0.12×10⁶ Kg/m²·s. Unfortunately, no appropriatematerials that have the required impedance are known in the field and sosome other approach is required.

[0010] While there are several proposed approaches to practicallyimprove the state of the art in acoustically matching two materialshaving disparate impedances, they all prove to be ad hoc and inefficientin energy transmission. The state of the art includes the use of a thin,approximately 10 microns in thickness, taut plastic film in which an airfilm is entrapped to cover the dry flat face of a 100 kHz transducer. A10-dB gain is reported for this approach without sacrifice of responsebandwidth. A different approach adds microscopic balloons to epoxy tocreate a low impedance matching material for the front face of atransducer. Improvements were reported for this case to frequencies ashigh as 1 MHz. The state of the art approaches typically include aspecial rubber material that, when fabricated into a quarter-wave layer,overcomes some of the transducer-to-air mismatch and a two-layermatching layer in which the best second layer is found when the firstlayer is not optimal. Typically, first layers consist of a rubber (e.g.,GE RTV615) containing air bubbles 50 microns in diameter. One suchapproach has an optimization criteria for a two layer matching layer inwhich the impedance steps monotonically from the source to the target.Although still not an optimal match, this method appears to providesbroader bandwidth performance over the preceding approaches. Anotherproposal has a non-monotonic multi-layer matching layer that proves tobe useful only for narrow-band matching. In another approach, many thinlayers of progressively increasing, or decreasing, impedance form, in acombined sense, the matching layer. In this approach, layers as small as{fraction (1/30)} of a wavelength make up the total matching layer. Oneapproach uses multiple layers of readily available materials toapproximately match 450 kHz transducers into air for non-contactnon-destructive testing of steel. Finally, in the U.S. Pat. No.6,311,573 issued to Mahesh Bhardwaj Nov. 6, 2001, there is described amatching layer, consisting of several layers, in which a standardpiezoelectric transducer is approximately matched to air. In a typicalexample, the piezoelectric lead-zirconate-titanate (PZT) member iscoated with aluminum, hard epoxy, and finally with clay-coated paper.Using Bhardwaj as a representative of the state of the art, Bhardwajprovides several ad hoc examples of matching a piezoelectric such as PZTto air. Bhardwaj describes in his Example 1 (col. 4, lines 38-57).

[0011] “A 1 MHz transducer may be constructed as follows:

[0012] Piezoelectric material: PZT.Z1=34×10⁶ Kg/m²·s;

[0013] First transmission layer: aluminum. V=6325 m/s.

[0014] Z2=17×10⁶ Kg/m²·s; P/8 @ 1 MHz=1000/8=125 ns, where 1000 ns isone period, P, for the MHz frequency. Therefore, thickness of this layeris 125×10−9×6,325,000=0.79 mm.

[0015] Second transmission layer: hard epoxy. V=2600 m/s. Z3=3×10⁶Kg/m²·s P/16 @ 1 MHz=1000/16=62.5 ns. Therefore, thickness of this layeris 62.5×10−9×2,600,000=0.16 mm. Facing layer: clay-coated paper. V=500m/s. Z4=0.6×10⁶ Kg/m²·s; P/16 @ 1 MHz=1000/16=62.5 ns. Therefore,thickness of this layer is 62.5×10−9×500,000=0.03 mm.”

[0016] In this particular example, three matching layers are used tomatch PZT with air. Table I below summarizes the impedance of thismethod where less than 20% of the energy is transferred from the PZT toair. TABLE I Impedance (Kg/m² · s) Source: Z₀ (PZT) 34 × 10⁶ FirstLayer: Z₁ 17 × 10⁶ Second Layer: Z₂  3 × 10⁶ Third Layer: Z₃ 0.6 × 10⁶ Target Medium: Z₅ (air) 415

[0017] Bhardwaj's Example 2 (col. 5, lines 1-16) has

[0018] “A transducer according to this invention with a multi-parttransmission layer might be constructed of the following layers:

[0019] piezoelectric layer (PZT) 34×10⁶ Kg/m²·s

[0020] aluminum layer 17×10⁶ Kg/m²·s

[0021] aluminum composite layer 7×10⁶ Kg/m²·s

[0022] epoxy layer 3×10⁶ Kg/m²·s

[0023] paper facing layer 0.3×106 Kg/m²·s”

[0024] Here four layers are used to match PZT to air. Table II belowsummarizes the impedances of Bhardwaj's Example 2 where the energytransferred is less than 20%. TABLE II Impedance (Kg/m² · s) Source: Z₀(PZT) 34 × 10⁶ First Layer: Z₁ 17 × 10⁶ Second Layer: Z₂  7 × 10⁶ ThirdLayer: Z₃  3 × 10⁶ Fourth Layer: Z₄ 0.3 × 10⁶  Target Medium: Z₅ (air)415

[0025] The above methods were all experimentally derived in an adhocmanner without any fundamental basis or analytical framework. Thereremains a need for manufacturing transducers and other acousticalsources consistently having optimal solutions to the matching betweensource and target impedances.

SUMMARY

[0026] The invention, in its several embodiments, includes a method ofmaking a transducer having a plurality of impedance matched layersincluding the steps of providing a piezoelectric element having a sourceimpedance, Z₀; selecting a target medium having a target impedance,Z_((N+1)); defining a number of matching layers, N, wherein N is aninteger greater than unity; and for each matching layer, J, incremented1 to the defined number of matching layer, N: determining a requiredimpedance according to a solution to the boundary value problem for Nlayers; selecting a material for matching layer J having substantiallythe determined required impedance Z_(J) wherein the selected materialfor matching layer J has a speed of sound and a wavelength λ_(J)associated with the speed of sound for matching layer J; determining apositive integer value, n_(J), and a thickness, L_(J), of the selectedmaterial for matching layer J and applying the matching layer J ofthickness L_(J) to the transducer.

[0027] The method of making a transducer having a plurality of impedancematched layers also includes: producing acoustical pressure by anacoustical source in a first medium having an acoustical impedance;measuring, by a receiving transducer, the acoustical pressure producedby the acoustic source in the first medium; producing acousticalpressure by the acoustical source in a second medium having anacoustical impedance; measuring, by the receiving transducer, theacoustical pressure produced by the acoustical source in the secondmedium; and determining the derived effective source impedance basedupon the acoustical impedance of the first medium, the acousticalimpedance of the second medium, the acoustical pressure in the firstmedium measured by the receiving transducer, and the acoustical pressurein the second medium measured by the receiving transducer.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] For a further understanding of the nature and objects of hepresent invention, reference should be made to the following detaileddescription, taken in conjunction with the accompanying drawings, inwhich like elements are given the same or analogous reference numbersand wherein:

[0029]FIG. 1 is a flowchart describing the preferred method embodimentof the present invention;

[0030]FIG. 2 illustrates an example layered transducing deviceembodiment according to the present invention; and

[0031]FIG. 3 is a flowchart describing the preferred method fordetermining an effective source impedance of the present invention.

DETAILED DESCRIPTION

[0032] The present invention in its several embodiments includestransducers having matching layers optimally matched in impedance andmethods of achieving the optimal matches. Each of the followingexamples, whether describing an interstitial media comprised of onelayer or several layers, describe interstitial media having an optimalmatch in impedances between a transducing source and a target medium. Inpractice, the number of layers chosen depends on the range and values ofimpedances desired for a particular implementation. The preferred methodof establishing optimal multiple matching layers extends the approachesrelying on the original boundary value problem formulation typicallyused for one layer. The methods and resulting products disclosed beloware for matching layers where the solved boundary value problem providesfor optimal solutions for two or more interposed layer and the method isextendable to N layers. The impedance values generated for each layerare optimal and when used to guide the material selection, provide formaximal energy transmission from the transducing source.

[0033] In case 1, a single layer is interposed between the source layerhaving an impedance, Z₀, and a target medium having an impedance, Z₂.The required impedance, Z₁, of the matched layer is determined bygenerating the product of the square roots of the impedance of Z₀ and ahaving an impedance Z₂ of the target medium. That is,

Z ₁=(Z ₀ Z ₂)^(1/2).  [3]

[0034] In case 2, two layers are interposed between the source layerhaving an impedance, Z₀, and a target medium having an impedance, Z₃.The required impedance of the matched first layer, Z₁, is determined bygenerating the product of the square of the cube root of the sourceimpedance of Z₀ and the cube root of the target medium impedance Z₂.That is,

Z₁=Z₀ ^(2/3)Z₃ ^(1/3).  [4]

[0035] Similarly, the required impedance of the matched second layer,Z₂, is determined by generating the product of the cube root of thesource impedance, Z₀, and the square of the cube root of the targetmedium impedance, Z₃. That is,

Z₂=Z₀ ^(1/3)Z₃ ^(2/3).  [5]

[0036] In case 3, three layers are interposed between the source layerhaving an impedance, Z₀, and a target medium having an impedance, Z₄.The required impedance of the matched first layer, Z₁, is determined bygenerating the product of the source impedance of Z₀ raised to the¾-power and the target medium impedance Z₄ raised to the ¼-power. Thatis,

Z₁=Z₀ ^(3/4)Z₄ ^(1/4).  [6]

[0037] Similarly, the required impedance of the matched second layer,Z₂, is determined by generating the product of the square root of thesource impedance, Z₀, and the square root of the target mediumimpedance, Z₄. That is,

Z₂=Z₀ ^(1/2)Z₄ ^(1/2).  [7]

[0038] Likewise, the required impedance of the matched third layer, Z₃,is determined by generating the product of the source impedance of Z₀raised to the ¼-power and the target medium impedance Z₄ raised to the¾-power. That is,

Z₃=Z₀ ^(1/4)Z₄ ^(3/4).  [8]

[0039] In case 4, four layers are interposed between the source layerhaving an impedance, Z₀, and a target medium having an impedance, Z₅.The required impedance of the matched first layer, Z₁, is determined bygenerating the product of the source impedance of Z₀ raised to the⅘-power and the target medium impedance Z₅ raised to the ⅕-power. Thatis,

Z₁=Z₀ ^(4/5)Z₅ ^(1/5).  [9]

[0040] Similarly, the required impedance of the matched second layer,Z₂, is determined by generating the product of the source impedance ofZ₀ raised to the ⅗-power and the target medium impedance Z₅ raised tothe ⅖-power. That is,

Z₂=Z₀ ^(3/5)Z₅ ^(2/5).  [10]

[0041] Likewise, the required impedance of the matched third layer, Z₃,is determined by generating the product of the source impedance of Z₀raised to the ⅖-power and the target medium impedance Z₅ raised to the⅗-power. That is,

Z₃=Z₀ ^(2/5)Z₅ ^(3/5).  [11]

[0042] Finally, the required impedance of the matched fourth layer, Z₄,is determined by generating the product of the source impedance of Z₀raised to the ⅕-power and the target medium impedance Z₅ raised to the⅘-power. That is,

Z₄=Z₀ ^(1/5)Z₅ ^(4/5).  [12]

[0043] Generally, the method of generating impedances for N layers,where N is a positive integer, interposed between the source layerhaving an impedance Z₀, and the target medium having an impedanceZ_(N+1), the impedance required for each successive interposed layer J,where J is an integer ranging from 1 to N, is generated as follows:

Z _(J) =Z ₀ ^([(N+1−J)/(N+1)]) Z _((N+1)) ^((J/N+1)).  [13]

[0044] A separate set of procedures, similar to those for a singlematching layer, determines the optimal thickness of the matching layersto insure maximum energy transfer across the matching layer. If thethickness of matching layer J is given by L_(J) and λ_(J) is thewavelength of sound in layer J, then

L _(J)=(2n _(J)−1)λ_(J)/4  [14].

[0045] where n_(J) is a positive integer that is preferably selected asunity, two or three in a balance between structural requirements andparasitic effects of the material. The single matching layer solution isconsistent with the case of a single matching layer described byEquation 2. The combination of the above procedures as an example method100 of making an acoustic transducer, or acoustical resonating source,having layers of optimally matched impedances is illustrated in FIG. 1.Preliminary selections and determinations 115 are made where thetransducing, acoustical resonating, source material is selected havingan impedance Z(0) and a resonance frequency, f(0). The target medium isdetermined and with it, its impedance Z(N+1). The number of matchinglayers, N, is determined. For purposes of iteration 125, the sourcematerial can be defined as layer J=0 120. For each matching layer, theimpedance of the matching layer is determined 135 from

Z _(J) =Z ₀ ^([(N+1−J)/(N+1)]) Z _((N+1)) ^((J/N+1));  [15]

[0046] The next step is selecting a material having the determinedimpedance Z (J) and having a wavelength, λ_(J), where the wavelength isdeterminable from the speed of sound of the material and thepiezoelectric resonant frequency of operation, f(0) 140. With thematerial selected and its structural and fabrication qualities known,the thickness integer, n(J) is determined 145. The thickness of theparticular layer J is then determined 150. The material of layer J isthen applied to the subsequent layer 155 where the piezoelectric mediumis treated as layer 0. The example method described is applicable toacoustical sources in addition to ultrasonic transducers. In thoseapplications, an effective source impedance is determined according to asteps disclosed below and the resulting effective source impedancereplaces 190 the known transducer impedance Z(0) 115.

[0047] The following examples illustrate the application of theabove-disclosed method in its several embodiments to making ultrasonictransducers having optimally matched acoustical impedances where theresulting transducer is illustrated by example in FIG. 2. The transducer200 is comprised of a PZT source layer in the preferred embodiment 210,whereupon a first layer 215, a second layer 220 and, if needed,successive layers up to the Nth layer 225 are applied in accordance withthe teachings of the present invention so that the acoustical energygenerated at the source 210 is efficiently transmitted to the targetmedium 230 due to the interstitial layers having optimally matchedimpedances.

[0048] First, in an application to the general case of matching atypical piezoelectric such as PZT to air, the piezoelectric has anexample impedance of 34×10⁶ Kg/m²·s and the target medium, air for thisexample, has an impedance of 415 Kg/m²·s. In fabricating a transducerwith a single matching layer using Equation 1, the matching layer wouldbe required to have an impractical impedance of 0.12×10⁶ Kg/m²·s. Infabricating a transducer with two matching layers then, using theteachings of the preferred method disclosed, one calculates that thefirst matching layer should be 0.78×10⁶ Kg/m²·s and the second matchinglayer should be 0.018×10⁶ Kg/m²·s. Selecting matching layer materialsmeeting these specifications insures an optimal configuration and thatthe maximal amount of energy will be transmitted into the target.

[0049] It should be clear to practitioners in the field that, from theabove example, increasing the number of matching layers increases therange of materials one may use in constructing an optimal transducer.For example, matching PZT to air using a single matching layer requiresa matching layer with an impedance of 0.12×10⁶ Kg/m²·s. Unfortunately, amaterial that seems to have the appropriate acoustical impedance is corkwhich also is very absorptive and therefore inappropriate for mostpractical applications. However, in fabricating a transducer with twomatching layers, one may choose materials with impedances of 0.78×10⁶Kg/M²·s and of 0.018×10⁶ Kg/m²·s such as those of various forms ofrubber which are materials that also have low attenuation coefficientswhereby such materials provide a practical means of matching PZT to air.

[0050] In an example where three matching layers are applied to thepresent invention, PZT is matched with air. Table III below summarizesthe results of the example method where the energy transferred is nearly100%. TABLE III Impedance (Kg/m² · s) Source: Z₀ (PZT) 34 × 10⁶ FirstLayer: Z₁  2 × 10⁶ Second Layer: Z₂ 0.12 × 10⁶   Third Layer: Z₃ 0.007 ×10⁶   Target Medium: Z₅ (air) 415

[0051] In the following example, four layers are used to match PZT toair. The table below summarizes the results of preferred the method ofthe present invention where nearly 100% of the energy is transferred.TABLE IV Impedance (Kg/m² · s) Source: Z₀ (PZT) 34 × 10⁶ First Layer: Z₁3.5 × 10⁶  Second Layer: Z₂ 0.37 × 10⁶   Third Layer: Z₃ 0.038 × 10⁶  Fourth Layer: Z₄ 0.004 × 10⁶   Target Medium: Z₅ (air) 415

[0052] The methods described above provide an effective and efficientmeans to match the acoustical impedances between two materials andthereby provide for the fabrication of ultrasonic transducers havingoptimally matched acoustical impedance. The ultrasonic transducersfabricated according to the teachings of this description provide formaximal energy transfer from the source of transduction to the targetmedium. Although the method, in its several embodiments, described hereprovides an optimal acoustical impedance match between any two materialsfor a specified number of layers, it is instructive to consider thematching of a typical piezoelectric such as PZT to air as described inthe examples given above. Disclosed are several specific implementationsof the general method. As above, the PZT has an acoustical impedance of34×10⁶ Kg/m²·s and the air has an impedance of 415 Kg/m²·s. If a singlematching layer is used, then the method reduces to the well knownclassical result described by Equations 1 and 2. For this case as shownabove, the matching layer would have an impedance of 0.12×10⁶ Kg/m²·s.As indicated above, cork is one of the few materials with suchimpedance. However, since this material is highly absorptive, i.e., agreat deal of acoustical energy will be lost, it is a poor candidate fora matching layer.

[0053] In moving to two matching layers as shown above, we haveimpedances of 0.78×10⁶ Kg/m²·s and 0.018×10⁶ Kg/m²·s. Various forms ofrubber are known to be fabricated to have such impedances. For example,hard rubbers can be constructed with an impedance of about 0.78×10⁶Kg/m2×s, a sound speed of about 2400 m/s, and a wavelength at 1 MHz of2.4 mm. The matching layer fabricated from this material could be assmall as a quarter of a wavelength, i.e., n_(J)=1, or 0.6 mm inthickness. Soft rubbers can be constructed with an impedance of about0.018×10⁶ Kg/m2×s, a sound speed of about 1050 m/s, and a wavelength at1 MHz of about 1 mm. The matching layer fabricated from this materialcould be as small as a quarter of a wavelength or 0.25 mm in thickness.

[0054] Moving to four matching layers, as described in the above TableIV, the following materials can be used: For the first layer, variousforms of plexiglass and TEFLON® are applicable for example to yield3.5×10⁶ Kg/m²·s; for the second layer, soft rubber yields 0.37×10⁶Kg/m²·s; for the third layer, forms of soft rubber yield 0.038×10⁶Kg/m²·s; and for the fourth layer, paper and forms of soft rubber yield0.004×10⁶ Kg/m²·s.

[0055] The thickness of each matching layer is determined by Equation 14with the matching layer thickness integer, n_(J), selected for eachlayer, J, for benefits including energy transfer efficiency and improvedmanufacturability.

[0056] The transducer example of the present invention is preferably aPZT device having a peak or resonant frequency where the preferredembodiment has one or more layers of soft rubber and/or one or morelayers of hard rubber painted onto either the transducer surface or asuccessive matching layer. The application of the rubber continues untila desired thickness of one-quarter wavelength where the wavelength is asdefined as the speed of sound in the rubber divided by the resonantfrequency of the piezoelectric element, see Equation 14. In addition tohard rubber painting, alternative embodiments have matching layersbonded to each other with conventional epoxies and cements andself-adhesive tape or other high viscosity epoxy, glue or cement.

[0057] Where it is not practicable to fabricate the material formatching layers to one-quarter wavelength or not desirable to fabricatethe material to as low as one-quarter wavelength due to structuralrequirements, then a matching layer thickness integer, n, greater thanone must be used. Where, for example n is 2, the matching layer isthree-fourths of a wavelength. It is clear to those skilled in the artthat by this disclosure, one can establish a resulting fabricationtarget total thickness of matching layers expressed approximately inwavelengths of similar but not necessarily identical material. That is,where λ₁ is approximately equal to λ₂, two one-quarter-wavelengthmatching layers maybe combined to achieve a one-half wavelength targetthickness. In doing so, one may approximately achieve a combinedthickness of one-half wavelength, λ₁/2. This method of targeting thethickness extends to higher target thickness as well. For example, atarget thickness of 3λ₂/2 may be desired where the first thickness is5λ₁/4 and the second thickness is λ₂/4, thereby yielding, for λ₁approximately equal to λ₂, a combined thickness of 3λ₁/2.

[0058] While PZT, i.e., lead zirconate titanate, is the preferredmaterial for the ultrasonic transducer or source, the method, in itsseveral embodiments, is applicable to any piezoelectric material as thesource material. Alternate materials include quartz, barium titanate,lithium sulfate, lithium niobate, lead meta-niobate as well as othersuitable electromechanical coupling agents. For the target medium, airand other gaseous media are anticipated to be the most common targets;however, liquids, including water and water-like media, as well assolids, including tissue and tissue-like materials, may also betargeted.

[0059] Although the examples given above are representative ofpiezoelectric devices operating in the MHz range of frequencies, thoseskilled in the art will recognize that the method is applicable to anypiezoelectric transducer operating over any range of frequencies. Thiswould include piezoelectric transducers operating in the kHz frequencyrange and even lower, as well as piezoelectric transducers fabricatedusing semiconductor techniques, deposition methods, and/ornano-technology methods, and operating in the megahertz (MHz), gigahertz(GHz), and the terahertz (THz) frequency ranges.

[0060] Although the method as described by example address piezoelectricdevices, those skilled in the art recognize that the method, in itsseveral embodiments, is applicable to any acoustical source orultrasonic transducer, regardless of the technique by which theacoustical wave is generated, provided that the effective acousticalimpedance, Z_(EFF), as defined below, is measured for the acousticalsource in question, and that the acoustical impedance of the source, Z₀,in the above analysis is replaced by Z_(EFF). The measurement of what wedefine as the effective acoustical impedance for an acoustical sourceenables the method detailed above by example, and applied to apiezoelectric source by example, to be applied to any acoustical sourceand to therefore optimally match any acoustical source to any medium ortarget of interest. In particular, the method may be applied tocapacitive as well as magneto-electric devices. It is applicable toloudspeakers, hearing aids, sirens, whistles, musical instruments, thatis, to any object that produces a sound wave.

[0061] Described next and in FIG. 3 is a series of experimentalmeasurements by which one determines the effective acoustical impedancefor any acoustical source to then be applied to the method of thepresent invention. Firstly, the source of interest is made to operate310 in a first medium or the medium of interest, i.e., the targetmedium, A, or in a medium with similar acoustical properties, A′, tothat of the target medium. For example, defining Z_(A) as the acousticalimpedance of the medium in which the source is operating, one presumesthat the impedance of medium A, Z_(A), is independently measurable andthat the source is not already optimally matched to this target. Using aseparate receiving transducer, one measures 315 the acoustical pressureproduced by the source of interest at an arbitrary location within themedium A, having impedance Z_(A). The receiving transducer need not beidentical or even similar to the source and it may well operate on verydifferent principles of sound production. It should, of course, operatewithin a range of frequencies and amplitudes appropriate to the source.The receiving transducer need not be calibrated to measure absolutepressure because relative measures of pressure will suffice. Althoughthe location of the receiver with respect to the source need not beprecisely defined, such measurements should follow good acousticalmeasurement practices and should be undertaken at sufficiently largeseparation distances so that near-field artifacts, known topractitioners in the field, do not pose a problem in corrupting themeasurements.

[0062] The pressure amplitude measured by the receiving transducer inmedium A, P_(RA), is given by

P _(RA) =p ₀ τ _(0A) =p ₀[2Z _(A)/(Z _(EFF) +Z _(A))];  [16]

[0063] where p₀ is the pressure at the source, τ_(0A) is thetransmission coefficient between the source and medium A, and Z_(EFF) isthe effective acoustical impedance of the source.

[0064] Next one replaces 320 medium A with a second medium, B, which hasacoustical properties that are different from A, or A′, but are stillappropriate for the function of both the acoustical source and thereceiving transducer. All other variables are preferably kept constant,e.g. distance between source transducer and receiving transducer remainthe same, and then the pressure amplitude is measured 325 at thereceiving transducer, P_(RB). The pressure amplitude measured by thereceiving transducer in medium B is given by

P _(R) B=p ₀τ_(0B) =p ₀[2Z _(B)/(Z _(EFF) +Z _(B))];  [17]

[0065] where τ_(0B) is the transmission coefficient between the sourceand medium B. While ensuring that the source is operating at the samepower levels whether medium A or B is in place, one takes the ratio ofthe above two equations which yields

P _(RA) /P _(RB)=[2Z _(A)/(Z _(EFF) +Z _(A))]/[2Z _(B)/(Z _(EFF) +Z_(B))].  [18]

[0066] Using the following definition for a variable, Ω,

Ω[P _(RA) /P _(RB) ]/[Z _(B) /Z _(A)],  [19]

[0067] one generates 330 the value for ZEFF according to the derivedrelationship,

Z _(EFF) [Z _(B) −ΩZ _(A)]/[Ω−1].  [20]

[0068] In the above example, the impedances of materials A and B areknown and it is through the process described above that the variable Ωis obtained empirically. Finally, making the identification that theeffective acoustical impedance is the acoustical impedance of the sourceone can exploit the method described above by the substitution ofZ_(EFF) for Z₀ 335, that is,

Z_(EFF)=Z₀  [21]

[0069] and the method described above and illustrated in FIG. 1 is usedto match any acoustical source to the medium or target of operation.

[0070] Two examples will illustrate how this experimental method is usedto determine the effective acoustical impedance of a given source andhow the invention, in its several embodiments, is be used to optimallymatch the source to its target material.

[0071] The first example is the case where there is a capacitivetransducer designed for operation in the ocean, particularly inseawater. Using an identical transducer as a receiver or a piezoelectrictransducer operating in a similar frequency range, one measures thepressure amplitude produced by the source in a seawater environment.Then one replaces the seawater with, say, distilled water, and repeatsthe measurement. These two measurements, together with the known theacoustical properties of seawater and distilled water allow for thedetermination of an effective acoustical impedance for the capacitivetransducer. Finally, using the example method or for calculatingappropriately matching layers in making an optimally matched transducer,one selects a series of coatings in terms of impedance and thickness,which, when applied to the source, provides an optimum acoustical matchbetween the transducer and the ocean. As previously explained, thisoptimal matching, in turn, allows the capacitive transducer to operateat its maximum efficiency.

[0072] As a second example, for a loudspeaker designed to operate in airover the frequency range of 5 to 10 kHz, one uses an appropriatemicrophone to measure the pressure produced by the loudspeaker operatingin air. Next, one measures the pressure produced by the loudspeakeroperating in an experimental chamber filled with nitrogen gas, forexample. These experimental measurements together with the above stepsfor determining an effective source impedance allows one to selectappropriate coatings in terms of im pedance and thickness for optimalacoustical matching, and, therefore, for optimal and efficientperformance.

[0073] Although the description above contains many specifications,these should not be construed as limiting the scope of the invention butas merely providing illustrations of some of the presently preferredembodiments of this invention.

[0074] Therefore, the invention has been disclosed by way of example andnot limitation, and reference should be made to the following claims todetermine the scope of the present invention.

I claim:
 1. A method of making a transducer having a plurality ofimpedance matched layers comprising: providing a piezoelectric elementhaving a source impedance, Z₀; selecting a target medium having a targetimpedance, Z_((N+1)); defining a number of matching layers, N, wherein Nis an integer greater than unity; and for each matching layer, J,incremented 1 to the defined number of matching layer, N: determining arequired impedance according to: Z _(J) =Z ₀ ^([(N+1−J)/(N+1)]) Z_((N+1)) ^((J/N+1)); selecting a material for matching layer J havingsubstantially the determined required impedance Z_(J) wherein theselected material for matching layer J has a speed of sound and awavelength λ_(J) associated with the speed of sound for matching layerJ; determining a positive integer value, N_(J), and a thickness, L_(J),of the selected material for matching layer J according to: L _(J)=(2n_(J)−1)λ_(J)/4; and applying the matching layer J of thickness L_(J) tothe transducer.
 2. A method of making a transducer having a plurality ofimpedance matched layers comprising: providing an acoustical sourcehaving a derived effective source impedance, Z_(EFF); selecting a targetmedium having a target impedance, Z_((N+1)); defining a number ofmatching layers, N, wherein N is an integer great than unity; and foreach matching layer, J, incremented 1 to the defined number of matchinglayer, N: determining a required impedance according to: Z _(J) =Z_(EFF) ^([(N+1−J)/(N+1)]) Z _((N+1)) ^((J/N+1)); selecting a materialfor matching layer J having substantially the determined requiredimpedance Z_(J) wherein the selected material for matching layer J has aspeed of sound and a wavelength λ_(J) associated with the speed of soundfor matching layer J; determining a positive integer value, n_(J), and athickness, L_(J), of the selected material for matching layer Jaccording to: L _(J)=(2n _(J)−1)λ_(J)/4; and applying the matching layerJ of thickness L_(J) to the transducer.
 3. The method of making atransducer having a plurality of impedance matched layers as claimed inclaim 2 further comprising: producing acoustical pressure by anacoustical source in a first medium having an acoustical impedance;measuring, by a receiving transducer, the acoustical pressure producedby the acoustic source in the first medium; producing acousticalpressure by the acoustical source in a second medium having anacoustical impedance; measuring, by the receiving transducer, theacoustical pressure produced by the acoustical source in the secondmedium; and determining the derived effective source impedance basedupon the acoustical impedance of the first medium, the acousticalimpedance of the second medium, the acoustical pressure in the firstmedium measured by the receiving transducer, and the acoustical pressurein the second medium measured by the receiving transducer.
 4. The methodof making a transducer having a plurality of impedance matched layers asclaimed in claim 3 wherein the step of determining the derived effectivesource impedance, Z_(EFF), is based upon the acoustical impedance of thefirst medium, Z_(A), the acoustical impedance of the second medium,Z_(B), the acoustical pressure in the first medium measured by thereceiving transducer, P_(RA), and the acoustical pressure in the secondmedium measured by the receiving transducer P_(RB), according to therelationship: Z _(EFF) =[Z _(B) −{[P _(RA) /P _(RB) ]/[Z _(B) /Z _(A)]}Z _(A) ]/[{[P _(RA) /P _(RB) ]/[Z _(B) /Z _(A)]}−1].
 5. An apparatusfor transmitting acoustical energy to a target medium having a targetimpedance, the apparatus comprising: a piezoelectric element having asource impedance, Z₀, and a plurality of matching layers; wherein eachof the plurality of matching layers, has a required impedance accordingto: Z _(J) =Z ₀ ^([(N+1−J)/(N+1)]) Z _((N+1)) ^((J/N+1)); and awavelength λ_(J) and wherein each of the plurality of matching layershas a thickness according to: L _(J)=(2n _(J)−1)λ_(J)/4, wherein n_(J)is a positive integer; and wherein the plurality of matching layers isbonded to the piezoelectric element.
 6. An article for matchingacoustical energy from a source having an impedance, Z₀^([(N+1−J)/(N+1)]), to a target medium having a target impedance,Z_((N+1)(J/N+1)), the article comprising: a plurality of matchinglayers, N, wherein each of the plurality of matching layers, J, has arequired impedance, Z_(J), according to: Z _(J) =Z ₀ ^([(N+1−J)/(N+1)])Z _((N+1)) ^((J/N+1);) and a wavelength λ_(J).
 7. The article as claimedin claim 6 wherein each of the plurality of matching layers has athickness according to: L _(J)=(2n _(J)−1)λ_(J)/4; and wherein N_(J) isa positive integer.
 8. The article as claimed in claim 6 wherein thetarget medium is air.